Question

If a snorkeler can develop a pressure in her lungs that is 10 kPa below the pressure outside her body, what is the longest snorkel she could use in the ocean?

Answer 1

longest snorkeler that can be used should be 0.995 m

Step-by-step explanation:

Given:

The pressure difference, P = 10 kPa = 10 × 10³ Pa

Let the maximum length of the snorkel that can be used be 'L'

Now,

The pressure difference should be equal to the pressure on the body due to the water.

The maximum depth of water that is exerting pressure on the body will be the length of the snorkeler

Thus, we know

pressure due to a depth 'L' of water is given as:

P' = ρgL

where, ρ is the density of the sea water = 1025 kg/m³

g is the acceleration due to gravity

now equating it with the pressure difference P

we get

ρgL = 10 × 10³ Pa

or

1025 × 9.8 × L = 10 × 10³

or

L = 0.995 m

Hence, the longest snorkeler that can be used should be 0.995 m